1. Field of the Invention
The present invention relates to a method of rolling tire simulation capable of simulating a situation of a tire rolling at a certain speed and of calculating it in shorter time with high accuracy.
2. Related Art
In recent years, a computer simulation is used for development of a tire. It is known that various method for simulating a rolling tire at a certain speed with the computer as disclosed in Japanese unexamined Published Applications Nos. 2003-127622, 2004-20229, 2004-322971, and 2002-67636. The computer simulation enables performance to some extent to be predicted without experimentally manufacturing the tire. As the computer simulation has been known, for example, a rolling simulation, in which a tire model is made to roll on a road model. Each model consists of the finite elements. Most of the finite elements are elements having similar elasticity to the rubber, cords and the like comprising a tire.
The tire model is given various boundary conditions such as a rim, inner pressure, and load, and contacts with the road model; and then, an accelerating step of accelerating the tire model up to a certain speed is conducted. As to the acceleration step, it takes approximately 1.4 seconds to accelerate to 50 km/h even when the tire model is accelerated sizably to 1 G (nearly equal to 9.8 m/s2) in view of actual service condition, for example. Then, after reaching the predetermined certain speed, necessary physical parameters are calculated from the rolling tire model.
For simulating characteristics of a tire rolling at a constant speed, the above-mentioned accelerating is wasted time. To shorten the amount of simulation time, it is effective to accelerate the tire model enormously and accelerates to a predetermined speed in a short time.
However, when the acceleration is too large, deformational amount of elastic elements of the tire model becomes notably large, and the elements may be damaged and calculation errors may occur.
The finite element method (FEM) is often used in the above-described simulation. In the finite element method, calculation runs by dividing time into short time steps. The state of each element at the end of a time step is adopted as initial values of a next time step, and the calculation is performed in chronological order. In each time step, some errors are observed since a calculation result is rounded off to a predetermined digits. Usually in the number of time steps, the number of digit is secured sufficiently not to affect the errors. However, the increase of acceleration time causes inevitably increases of the number of time steps, thereby possibly accumulating errors and reducing accuracy of calculation, so called underflow.